**Carl Friedrich Gauss** worked in a wide variety of fields in both mathematics and physics incuding number theory, analysis, differential geometry, geodesy, magnetism, astronomy and optics. His work has had an immense influence in many areas.

- His teacher, Büttner, and his assistant, Martin Bartels, were amazed when Gauss summed the integers from 1 to 100 instantly by spotting that the sum was 50 pairs of numbers each pair summing to 101.
- In 1788 Gauss began his education at the Gymnasium with the help of Büttner and Bartels, where he learnt High German and Latin.
- After receiving a stipend from the Duke of Brunswick- Wolfenbüttel, Gauss entered Brunswick Collegium Carolinum in 1792.
- At the academy Gauss independently discovered Bode's law, the binomial theorem and the arithmetic- geometric mean, as well as the law of quadratic reciprocity and the prime number theorem.
- In 1795 Gauss left Brunswick to study at Göttingen University.
- Gauss's teacher there was Kästner, whom Gauss often ridiculed.
- Gauss returned to Brunswick where he received a degree in 1799.
- After the Duke of Brunswick had agreed to continue Gauss's stipend, he requested that Gauss submit a doctoral dissertation to the University of Helmstedt.
- Gauss's dissertation was a discussion of the fundamental theorem of algebra.
- With his stipend to support him, Gauss did not need to find a job so devoted himself to research.
- In June 1801, Zach, an astronomer whom Gauss had come to know two or three years previously, published the orbital positions of Ceres, a new "small planet" which was discovered by G Piazzi, an Italian astronomer on 1 January, 1801.
- Zach published several predictions of its position, including one by Gauss which differed greatly from the others.
- When Ceres was rediscovered by Zach on 7 December 1801 it was almost exactly where Gauss had predicted.
- Although he did not disclose his methods at the time, Gauss had used his least squares approximation method.
- In June 1802 Gauss visited Olbers who had discovered Pallas in March of that year and Gauss investigated its orbit.
- Olbers requested that Gauss be made director of the proposed new observatory in Göttingen, but no action was taken.
- Gauss began corresponding with Bessel, whom he did not meet until 1825, and with Sophie Germain.
- In 1807 Gauss left Brunswick to take up the position of director of the Göttingen observatory.
- Gauss arrived in Göttingen in late 1807.
- Gauss's work never seemed to suffer from his personal tragedy.
- Gauss's contributions to theoretical astronomy stopped after 1817, although he went on making observations until the age of 70.
- Much of Gauss's time was spent on a new observatory, completed in 1816, but he still found the time to work on other subjects.
- In fact, Gauss found himself more and more interested in geodesy in the 1820s.
- Gauss had been asked in 1818 to carry out a geodesic survey of the state of Hanover to link up with the existing Danish grid.
- Gauss was pleased to accept and took personal charge of the survey, making measurements during the day and reducing them at night, using his extraordinary mental capacity for calculations.
- Because of the survey, Gauss invented the heliotrope which worked by reflecting the Sun's rays using a design of mirrors and a small telescope.
- Gauss often wondered if he would have been better advised to have pursued some other occupation but he published over 70 papers between 1820 and 1830.
- In 1822 Gauss won the Copenhagen University Prize with Theoria attractionis Ⓣ(Theory of attraction)...
- From the early 1800s Gauss had an interest in the question of the possible existence of a non-Euclidean geometry.
- Gauss confided in Schumacher, telling him that he believed his reputation would suffer if he admitted in public that he believed in the existence of such a geometry.
- Gauss had a major interest in differential geometry, and published many papers on the subject.
- In fact, this paper rose from his geodesic interests, but it contained such geometrical ideas as Gaussian curvature.
- The period 1817-1832 was a particularly distressing time for Gauss.
- Gauss, however, never liked change and decided to stay in Göttingen.
- Gauss had known Weber since 1828 and supported his appointment.
- Gauss had worked on physics before 1831, publishing Über ein neues allgemeines Grundgesetz der Mechanik Ⓣ(On a new general fundamental law of mechanics), which contained the principle of least constraint, and Principia generalia theoriae figurae fluidorum in statu aequilibrii Ⓣ(General principles of the theory of the shape of fluids in a state of equilibrium) which discussed forces of attraction.
- These papers were based on Gauss's potential theory, which proved of great importance in his work on physics.
- In 1832, Gauss and Weber began investigating the theory of terrestrial magnetism after Alexander von Humboldt attempted to obtain Gauss's assistance in making a grid of magnetic observation points around the Earth.
- Gauss was excited by this prospect and by 1840 he had written three important papers on the subject: Intensitas vis magneticae terrestris ad mensuram absolutam revocata Ⓣ(Measurement of the absoute intensity of terrestrial magnetic force revisited) (1832), Allgemeine Theorie des Erdmagnetismus Ⓣ(General theory of geomagnetism) (1839) and Allgemeine Lehrsätze in Beziehung auf die im verkehrten Verhältnisse des Quadrats der Entfernung wirkenden Anziehungs- und Abstossungskräfte Ⓣ(General theorems in relation to the acting in perverse circumstances of the square of the distance of attraction and repulsion) (1840).
- Gauss used the Laplace equation to aid him with his calculations, and ended up specifying a location for the magnetic South pole.
- However, once Gauss's new magnetic observatory (completed in 1833 - free of all magnetic metals) had been built, he proceeded to alter many of Humboldt's procedures, not pleasing Humboldt greatly.
- However, Gauss's changes obtained more accurate results with less effort.
- Gauss and Weber achieved much in their six years together.
- However, this was just an enjoyable pastime for Gauss.
- The Magnetischer Verein Ⓣ(Magnetic Society) and its journal were founded, and the atlas of geomagnetism was published, while Gauss and Weber's own journal in which their results were published ran from 1836 to 1841.
- Gauss spent the years from 1845 to 1851 updating the Göttingen University widow's fund.
- Two of Gauss's last doctoral students were Moritz Cantor and Dedekind.
- Gauss presented his golden jubilee lecture in 1849, fifty years after his diploma had been granted by Helmstedt University.
- From the mathematical community only Jacobi and Dirichlet were present, but Gauss received many messages and honours.
- From 1850 onwards Gauss's work was again nearly all of a practical nature although he did approve Riemann's doctoral thesis and heard his probationary lecture.
- His health deteriorated slowly, and Gauss died in his sleep early in the morning of 23 February, 1855.

Born 30 April 1777, Brunswick, Duchy of Brunswick (now Germany). Died 23 February 1855, Göttingen, Hanover (now Germany).

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Algebra, Ancient Greek, Ancient Indian, Astronomy, Geometry, Group Theory, Knot Theory, Origin Germany, Number Theory, Physics, Puzzles And Problems, Special Numbers And Numerals, Topology

Parts: 1 2

Sections: 3

Theorems: 4

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive